In the statistical part of this research, we assume that the processes \(M_t\)  and \(S_t\)  are observed on the equidistant grid \( t=0, \Delta , ..., n \Delta \)  with some fixed \(\Delta >0.\)  For the Lévy - based models this case is essentially more difficult than the case of high - frequency data (i.e., the case \(\Delta \rightarrow 0\)  as \(n \rightarrow \infty \) ), see, e.g., the papers by Belomestny and his coauthors ([1]}, [2]}, [3]}, [4]}), Neumann and Reiss ([5]}), Comte and Genon-Catalot ([6]}), Gugushvili ([7]}). Nevertheless, this kind of data allows to avoid the difficulties raised by the unclear behaviour of the delay parameter (see above), since we consider the increments of prices over some fixed intervals, and it is not important whether the changes in the Bitcoin prices cause the changes in media attention, or vice versa.
